# Lesson Worksheet: Triangles and Coordinate Proofs Mathematics

In this worksheet, we will practice finding the vertices and side lengths of a triangle on the coordinate plane and using them to write a coordinate proof.

**Q1: **

Give the coordinates of the vertices , , and .

- A, ,
- B, ,
- C, ,
- D, ,
- E, ,

**Q2: **

Give the coordinates of the vertices and .

- A
- B
- C
- D
- E

**Q3: **

An isosceles triangle has vertices , , and . Find the length of the line segment drawn from to which is perpendicular to .

- A length units
- B length units
- C length units
- D length units

**Q4: **

A triangle is drawn in the coordinate plane with its vertices at , , and .

Find the length of the base .

Find the height of the triangle.

Hence, find the area of the triangle.

- A12.5 square units
- B25 square units
- C6.25 square units
- D10 square units
- E22.5 square units

**Q5: **

Given that is an isosceles triangle, where the coordinates of the points , , and are , , and , find the area of .

**Q6: **

A triangle has vertices at the points , , and with coordinates , , and respectively.

Work out the perimeter of the triangle . Give your solution to two decimal places.

Work out the area of the triangle .

**Q7: **

A triangle has vertices at the points , , and with coordinates , , and respectively.

Work out the perimeter of the triangle . Give your solution to one decimal place.

By drawing a rectangle through the vertices of the triangle, or otherwise, work out the area of the triangle .

**Q8: **

A triangle has vertices at the points , , and with coordinates , , and respectively. Work out the area of the triangle .

**Q9: **

A triangle has vertices at the points , , and with coordinates , , and respectively. Work out the perimeter of the triangle . Give your solution to two decimal places.

**Q10: **

Find the length of the base of Triangle B.